Another proof of Seymour's 6-flow theorem (Q6565818)
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scientific article; zbMATH DE number 7874809
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Another proof of Seymour's 6-flow theorem |
scientific article; zbMATH DE number 7874809 |
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Another proof of Seymour's 6-flow theorem (English)
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2 July 2024
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One of the longstanding conjectures of Tutte states that every 2-edge-connected graph has a nowhere zero 5-flow. \textit{P. D. Seymour} [J. Comb. Theory, Ser. B 30, 130--135 (1981; Zbl 0474.05028)] proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero 6-flow, utilizing a nowhere-zero flow valued in the group \({\mathbb Z}_2 \times {\mathbb Z}_3\). A new short proof of a generalization of this theorem, where \({\mathbb Z}_2 \times {\mathbb Z}_3\)-valued functions are found subject to certain boundary constraints.
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6-flow theorem
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group-valued flow
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nowhere-zero flow
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